Search NASA⌕ Search

SEARCH · Search NASA

Results for “three space dimension”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Numerical simulation in three space dimensions of time-dependent thermal convection in a rotating fluid

Three-dimensional time-dependent convection in a plane layer of fluid, uniformly heated from below and subject to vertical shear and to rotation about an axis tilted from the vertical, was simulated by the numerical solution of the Boussinesq equations, including all Coriolis terms. Rotation about a vertical axis produces smaller convection cells with diminished heat fluxes and considerable vorticity. When the rotation axis is tilted from the vertical to represent tropical latitudes, the convection cells become elongated in a N-S direction. Imposed flows with constant vertical shear produce convective rolls aligned with the mean flow. When the rotation vector is tilted from the vertical, the competing effects due to rotation and shear can stabilize the convective motions.

Hathaway, D. H.↗

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

Bryson, Steve↗

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗

Space-Time Localization of Plasma Turbulence Using Multiple Spacecraft Radio Links

Space weather is described as the variability of solar wind plasma that can disturb satellites and systems and affect human space exploration. Accurate prediction requires information of the heliosphere inside the orbit of the Earth. However, for predictions using remote sensing, one needs not only plane-of-sky position but also range information the third spatial dimension to show the distance to the plasma disturbances and thus when they might propagate or co-rotate to create disturbances at the orbit of the Earth. Appropriately processed radio signals from spacecraft having communications lines-of-sight passing through the inner heliosphere can be used for this spacetime localization of plasma disturbances. The solar plasma has an electron density- and radio-wavelength-dependent index of refraction. An approximately monochromatic wave propagating through a thin layer of plasma turbulence causes a geometrical-optics phase shift proportional to the electron density at the point of passage, the radio wavelength, and the thickness of the layer. This phase shift is the same for a wave propagating either up or down through the layer at the point of passage. This attribute can be used for space-time localization of plasma irregularities. The transfer function of plasma irregularities to the observed time series depends on the Doppler tracking mode. When spacecraft observations are in the two-way mode (downlink radio signal phase-locked to an uplink radio transmission), plasma fluctuations have a two-pulse response in the Doppler. In the two-way mode, the Doppler time series y2(t) is the difference between the frequency of the downlink signal received and the frequency of a ground reference oscillator. A plasma blob localized at a distance x along the line of sight perturbs the phase on both the up and down link, giving rise to two events in the two-way tracking time series separated by a time lag depending the blob s distance from the Earth: T2-2x/c, where T2 is the two-way time-of-flight of radio waves to/from the spacecraft and c is the speed of light. In some tracking situations, more information is available. For example, with the 5-link Cassini radio system, the plasma contribution to the up and down links, y(sub up)(t) and y(sub dn)(t), can be computed separately. The times series y(sub up)(t) and y(sub dn)(t) respond to a localized plasma blob with one event in each time series. These events are also separated in time by T2-2x/c. By cross-correlating the up and down link Doppler time series, the time separation of the plasma events can be measured and hence the plasma blob s distance from the Earth determined. Since the plane-of-sky position is known, this technique allows localization of plasma events in time and three space dimensions.

Armstrong, John W.↗

Application of a novel finite difference method to dynamic crack problems

A versatile finite difference method (HEMP and HEMP 3D computer programs) was developed originally for solving dynamic problems in continuum mechanics. It was extended to analyze the stress field around cracks in a solid with finite geometry subjected to dynamic loads and to simulate numerically the dynamic fracture phenomena with success. This method is an explicit finite difference method applied to the Lagrangian formulation of the equations of continuum mechanics in two and three space dimensions and time. The calculational grid moves with the material and in this way it gives a more detailed description of the physics of the problem than the Eulerian formulation.

Chen, Y. M.↗

Treatment of cloudiness in regional scale - Numerical weather prediction models

A numerical weather prediction model is considered in which cloud water and precipitation are explicitly predicted as functions of three space dimensions and time. Approximations in the thermodynamic and continuity equations are discussed in detail, as well as the cumulus parameterization and the cloud microphysics parameterization. An example of a real-data forecast indicates that very accurate quantitative precipitation and cloud cover forecasts are possible using initial observations from only the relatively sparse rawinsonde network in the U.S.

Kreitzberg, C. W.↗

On the practical use of high-order methods for hyperbolic systems

The paper tests a number of high order methods on a variety of dynamic problems in one, two, and three space dimensions. The problems covered include wave propagation phenomena as well as an asymptotic approach to a steady state. Consideration is given to both smooth and shocked flows. It is shown that the methods compared require only minor modifications of many existing second-order schemes. Further, the results show that significant gains can be expected from the use of fourth-order methods. Finally, spectral methods are also considered for some of the problems presented.

Turkel, E.↗

Criteria for fragmentation in a collapsing rotating cloud

The isothermal collapse of a rotating protostar with pressure and self-gravity is calculated by a hydrodynamic computer code that treats three space dimensions. A number of initial conditions are tested to determine the conditions under which a cloud is unstable to fragmentation. It is shown that fragmentation does not proceed to a significant extent during the first free-fall time, but that in most cases fragmentation has occurred by 1.5 to 2 times the initial free-fall time. The extent to which the density in the fragments is enhanced over that in their surroundings on this time scale depends on the initial ratio of thermal to gravitational energy, but is only weakly dependent on the type and amplitude of the perturbation and on the initial rotational energy.

Bodenheimer, P.↗

Fragmentation in a rotating protostar - A re-examination of comparison calculations

The self-gravitating collapse of a rotating, isothermal protostellar cloud has been recalculated with two independent fluid-dynamic computer codes, in three space dimensions, with improved spatial resolution compared to previous calculations. The results again predict fragmentation and formation of a binary protostellar system with properties similar to those obtained in the lower-resolution calculations. The results, however, are in disagreement with those obtained with a particle-dynamic code by Gingold and Monaghan (1981) for the collapse of a cloud from the same initial conditions. Possible explanations for the divergent results are discussed.

Bodenheimer, P.↗

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

The shape, propagation and mean-flow interaction of large-scale weather systems

In investigations concerned with obtaining an understanding of the general circulation of the atmosphere, the determination of the role of the large-scale eddies presents a special problem. In the present study,attention is given to a theory which, in some ways, provides an extension of the Eliassen-Palm flux concept so that it can be applied in particular to the time-averaged three space dimension problem. Particular emphasis is given to the understanding of the feedback of the eddies onto the mean flow. However, the behavior of the eddies themselves is also discussed. It is shown that, in simple situations, the anisotropic eddy horizontal velocity correlation tensor implies the shape and propagation of eddies and the feedback of the eddies onto the mean flow.

Hoskins, B, J.↗

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Leveque, R. J.↗

Accuracy of schemes for the Euler equations with non-uniform meshes

The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given.

Turkel, E.↗

Accuracy of schemes for the Euler equations with non-uniform meshers

The effect of nonuniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme is considered based on a finite volume formuation. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are pesented in both two- and three-space dimensions. Applications to finite difference and impicit algorithms are also given.

Turkel, E.↗

Flux-split algorithms for the multi-dimensional Euler equations with real gases

Upwind algorithms are developed for the numerical solution of the multidimensional Euler equations for real gases. Flux-splitting methods are derived which account for a general equation of state. Approximations to the state equation based on physical arguments result in simplified algorithms which may be implemented into existing perfect-gas codes. Applications of the method to several high-Mach-number high-temperature flows are presented for two and three space dimensions.

Grossman, B.↗

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

Aerothermal environment induced by mismatch at the SSME main combustion chamber-nozzle joint

The computational study reported here is motivated by a Space Shuttle main engine hardware problem detected in post-flight and post-test inspections. Of interest are the potential for hot gas ingestion into the joint (G15) at the main combustion chamber-to-nozzle interface and the effect of particular goemetric nonuniformities on that gas ingestion. The flowfield in the G15 region involves supersonic flow past a rounded forward facing step preceded by a deep narrow cavity. This paper describes the physical problem associated with joint G15 and computational investigations of the G15 aerothermal environment. The associated flowfield was simulated in two and three space dimensions using the United Solutions Algorithm (USA) computational fluid dynamics code series. A benchmark calculation of experimentally measured supersonic flow over of a square cavity was performed to demonstrate the accuracy of the USA code in analyzing flows similar to the G15 computational flowfield. The G15 results demonstrate the mechanism for hot gas ingestion into the joint and reveal the sensitivity to salient geometric nonuniformities.

Mcconnaughey, H. V.↗